This is mentioned as being difficult at lunchtimes, bars not serving food and bakers shutting at 11-30 'til 16-00. Whilst I can't vouch for the whole of France this is mostly incorrect. The bakers will normally be open until 13-30 and reopen at 16-00.
A bar will often be just that, no food served at any time. There are many small family bar/ restaurants that serve food at lunchtime. The thing to seek out a place advertising 'Menu Ouvrier', this is the 'working class lunch' . You can get an excellent meal (3 courses) for 12- 14 €. Often these places look very humble from the outside but don't be put off.
For me you can keep the fancy priced restaurants, give me one of these small places every time, nourishing food, just what you need.